rus
Issue #4/2025
E. A. Kovaleva, L. V. Begunovich, M. M. Korshunov
Time-dependent DFT-based Study of Bacteriochlorophyll a Optical Properties within the B800 part of Rhodoblastus Acidophilus Light-Harvesting Complex
Time-dependent DFT-based Study of Bacteriochlorophyll a Optical Properties within the B800 part of Rhodoblastus Acidophilus Light-Harvesting Complex
DOI: 10.22184/1993-7296.FRos.2025.19.4.304.311
Time-dependent density functional theorybased approaches, TD-DFT and TD-DFTB, are
used to study the optical absorption of B800 part of light-harvesting complex 2 (LH2) of
Rhodoblastus acidophilus. Calculated spectra for both single molecule and the optimized
structure of B800 complex containing nine of such molecules are in qualitative agreement
with experimental data. The absence of any sizable effects originating from the interaction
between adjacent molecules are proved. Thus, optical features of B800 LH2 part are
not connected to the structural organization of pigments. The importance of the timedependent procedure for the correct description of BChl a absorption spectrum is demonstrated.
Time-dependent density functional theorybased approaches, TD-DFT and TD-DFTB, are
used to study the optical absorption of B800 part of light-harvesting complex 2 (LH2) of
Rhodoblastus acidophilus. Calculated spectra for both single molecule and the optimized
structure of B800 complex containing nine of such molecules are in qualitative agreement
with experimental data. The absence of any sizable effects originating from the interaction
between adjacent molecules are proved. Thus, optical features of B800 LH2 part are
not connected to the structural organization of pigments. The importance of the timedependent procedure for the correct description of BChl a absorption spectrum is demonstrated.
Optical Properties of the Bacteriochlorophyll a Within the B800 Part of Rhodoblastus Acidophilus
Light-Harvesting Complex Studied
Via Time-Dependent Density Functional Theory-Based Calculations
E. A. Kovaleva 1, L. V. Begunovich 1, M. M. Korshunov 1, 2
Federal Research Center Krasnoyarsk Science Center SB RAS, Krasnoyarsk, Russia
Kirensky Institute of Physics, Federal Research Center Krasnoyarsk Science Center SB RAS, Krasnoyarsk, Russia
Time-dependent density functional theory-based approaches, TD-DFT and TD-DFTB, are used to study the optical absorption of B800 part of light-harvesting complex 2 (LH2) of Rhodoblastus acidophilus. Calculated spectra for both single molecule and the optimized structure of B800 complex containing nine of such molecules are in qualitative agreement with experimental data. The absence of any sizable effects originating from the interaction between adjacent molecules are proved. Thus, optical features of B800 LH2 part are not connected to the structural organization of pigments. The importance of the time-dependent procedure for the correct description of BChl a absorption spectrum is demonstrated.
Keywords: light-harvesting complex, purple bacteria, DFT, DFTB, TD-DFT, optical absorption spectra
Article received: 11.02.2025
Article accepted: 24.03.2025
1. Introduction
Photosynthesis is attracting much attention all around the world for decades. A key step in providing energy for subsequent biochemical reactions is the absorption of light by structures called light-harvesting (LH) complexes consisting of pigments linked by protein chains, see reviews [1–3]. LH2 peripheral light-harvesting complexes from the purple bacterium Rhodoblastus acidophilus is a widely used model object for studying LH absorption spectra [4–6] due to its relatively simple structure with the C9 symmetry, consisting of nine rhodopin β-D-glucoside and twenty-seven bacteriochlorophyll a (BChl a) molecules, linked into a single system by eighteen alternating amino acid chains. BChl a molecules are organized into two subsystems: the first subsystem is a close-packed ring of eighteen BChl a molecules oriented with porphyrin fragments along the symmetry axis of the structure, and the second subsystem is a loosely packed ring of nine BChl a molecules with porphyrin planes located perpendicular to the symmetry axis. The indicated subsystems are responsible for the characteristic peaks in the LH2 optical absorption spectrum, including the near-infrared absorption peaks, such as the Qy absorption peaks of BChl a molecules at 850 nm and 800 nm (the corresponding molecular subsystems are denoted as B850 and B800). As an alternative to the commonly used QM / MM approach, we propose it a simplified model to reproduce the LH2 optical properties. To study the LH system, as a first step, we model the B800 ring due to its simpler structure. The results obtained can be further utilized to construct more complex models and describe other parts of the LH complex.
Light-harvesting complexes are known to be difficult to characterize because interactions between pigments can lead to appearance of excitons in the system, as demonstrated for the B850 ring of the LH2 structure [7, 8]. Previously, possible exciton effects were not taken into account to create the LH2 model [9], since the emergence of collective excited states in the B800 ring is extremely unlikely due to the large distance between BChl a molecules [10]. It is assumed that the shift in the Qy peak position of B800 relative to that of the BChl a molecule is caused by the structure distortion of the magnesium-porphyrin fragments caused by interaction with protein residues. The present study is aimed to support this assumption using time-dependent (TD) calculations within the density functional theory (DFT) framework.
2. Computational methods
and models
The experimentally obtained 2FKW PDB structure [11] was used as a basis for our calculations, from which nine BChl a molecules forming the B800 ring were taken. The surrounding protein chains or their fragments were not included in the model to exclude the influence of the amino acid environment on the pigments, which made it possible to estimate the direct interaction between neighboring BChl a molecules. For comparison, the structure of an isolated pigment molecule was also calculated. Both structures were fully optimized until the forces acting on the atoms became less than 2 · 10−4 Hartree / bohr. The calculations were carried out in the DFTB+ software package using the DFTB3 version of the DFTB method, the standard set of 3OB parameters and the D3 correction for van-der-Waals interactions.
It has been previously found that the Hartree-Fock (HF) exchange has a significant effect on the optical properties of BChl a [9], therefore the hybrid exchange-correlation functional HSE06 was chosen for TD-DFT calculations in the VASP software package. The calculations were conducted under periodic boundary conditions. The lattice vector b was set to match the experimental distance between adjacent molecules in the B800 ring, which is 21.1 Å. A vacuum layer was introduced in other directions to prevent any artificial interactions between neighboring cells. The BChl a molecule was fully optimized using the GGA-PBE functional. The resulting structure was then used for hybrid calculations. The calculations employed a plane wave basis with a cutoff energy of 400 eV and the PAW method. Given the large size of the unit cell used in the calculations, computations at the Г-point is appropriate due to being both efficient and sufficient for an accurate description of the model.
To calculate the absorption coefficient, three different methods were applied depending on the software used. Due to the large number of atoms in the B800 ring system, only the TD-DFTB method was appropriate for its analysis. For the isolated BChl a molecule, both DFTB and standard DFT methods were utilized.
To calculate optical properties in VASP, the frequency-dependent dielectric matrix is determined. The absorption coefficient is calculated using the following formula:
σ(ω) = , (1)
where ε'(ω) and ε"(ω) are the real and imaginary parts of the dielectric function, and ω is the frequency. This approach is based on ground state calculations and does not include excited states. To address this limitation, a time-dependent (TD) procedure is required. The linear-response TD method involves solving the Casida equation:
Ω FI = ω2 FI , (2)
where Ω is the response matrix that depends on the occupied and virtual Kohn-Sham orbitals and the energy difference between them (ω), and FI is the eigenvector found by solving equation (2), which is used to calculate the oscillator strength.
The DFTB+ package implements both the Casida method and the real-time propagation of electron dynamics (ED). The time-dependent dipole moment µ depends on the electric field E as follows [12]:
µ(ω) = α E(ω), (3)
where α is the polarizability tensor. Imaginary part of the tensor trace α is proportional to the optical absorption coefficient:
σ(ω) = Im Tr (α). (4)
Here and below, calculations using the Casida method are marked as TD regardless of methods for the electronic structure calculations while the real-time propagation of electron dynamics is denoted as ED. HSE06 notation without indication of TD calculation corresponds to the calculation of the absorption coefficient from the frequency-dependent dielectric matrix.
3. Results and discussion
Previously discussed calculations of BChl a absorption spectrum [9] show the comparability of results obtained by hybrid DFT and parameterized DFTB3 method. The absorption spectrum contains both Soret peaks around 350 nm and characteristic peaks in the Q region. To describe the large molecular assemblies of more complicated LH2 models, the DFTB3 method is preferable due to its computational efficiency. The absorption spectrum of the B800 ring, consisting of nine BChl a molecules is identical to the spectrum of the isolated molecule (fig. 1) in the absence of an amino acid environment. The absorption peak Qy is located around 700 nm that is significantly different from the experimentally observed 800 nm, thus confirms our suggestion of the absence of any sizable interaction between molecules in B800 ring. Further the energies and intensities of optical transitions were obtained by solving the Casida equation within the DFTB and HSE06 electronic structure calculation methods (fig. 2).
The absorption spectra obtained by the TD-DFTB method are in agreement with the ED calculations and literature data, indicating the well-chosen and well-tested interatomic interaction parameters specifically designed to reproduce the properties of Mg-porphyrin compounds like chlorophyll. Only the lowest energy transition was calculated for the B800 ring corresponding to the Qy peak in order to save computational resources, since a large number of forbidden transitions with zero intensity significantly slow down the calculation. The obtained value of the Qy peak position is consistent with the data obtained by other methods (see Table 1). Thus, the bathochromic shift of the Qy peak in the absorption spectrum of B800 is entirely due to structural distortions rising from van-der-Waals interactions with protein chains.
It should be noted that TD-HSE06 calculation gives significant hypsochromic shift of both absorption peaks in the Q-region compared to those calculated from the frequency-dependent dielectric matrix. That indicates the need to carry out the non-stationary calculations for description of the optical properties of BChl a and similar pigments. In Figure 3, we demonstrate the absorption spectra of BChl a molecular calculated within DFTB3 and HSE06 approaches, as well as the results of DFTB calculations for the B800 ring. The position of Qy absorption peak is of particular interest since this peak is a characteristic feature of LH2 spectrum as a whole. All non-stationary calculations show close values of the Qy peak, located in the range of ~660–680 nm, while TD-HSE06 overestimates the transition energy for Qx peak (see Table 1).
4. Conclusion
Time-dependent DFT-based methods, DFTB3 and HSE06, were used to study the absorption spectra of BChl a molecule as the part of B800 ring of the LH2 complex of Rhodoblastus acidophilus. 1) It is shown that despite the absence of the collective excitations in the B800 system, the absence of any sizable effects connected to the interaction between pigments confirms the conjecture that the optical features of B800 are determined by the protein surroundings, not by their structural organization. 2) Use of the time-dependent calculations is necessary for the correct description of BChl a molecule absorption spectra since the ground state calculations underestimate the position Qy peak energy by 170 nm. 3) DFTB method gives reasonable results comparable to hybrid DFT method and may be used to model the larger systems containing magnesium-porphyrin compounds.
Acknowledgement
We thank V. F. Shabanov for useful discussions. Authors would like to thank Information Technology Centre, Novosibirsk State University for providing access to their supercomputers. L. V. Begunovich would like to thank Irkutsk Supercomputer Center of SB RAS for providing the access to HPC-cluster “Akademik V. M. Matrosov” (Irkutsk Supercomputer Center of SB RAS, Irkutsk: ISDCT SB RAS; http://hpc.icc.ru)
Authors contribution
E. A. Kovaleva – calculations, data processing, discussion, writing; L. V. Begunovich – resources, calculations, discussion; M. M. Korshunov – conceptualization, discussion, writing.
Funding
This work was supported by the state assignment of the Ministry of Science and Higher Education of the Russian Federation.
Conflict of interest
Authors declare no potential conflict of interest.
AUTHORS
Kovaleva Evgeniya A., Cand. of Sciences (Phys.&Math), e-mail: kovaleva.evgeniya1991@mail.ru; Senior Researcher, FITZ «Krasnoyarsk Scientific Center SB RAS», Krasnoyarsk, Akademgorodok, Russia.
ORCID 0000-0002-8008-0906
Begunovich Lyudmila V., Cand. of Sciences (Phys.&Math), Researcher, FITZ «Krasnoyarsk Scientific Center SB RAS», Krasnoyarsk, Akademgorodok, Russia.
ORCID 0000-0002-8103-1823
Korshunov Maxim M., Dr. of Sciences (Phys.&Math), Corr. Member of the RAS; Chief Researcher, L. V. Kirensky Institute of Physics of the RAS – a separate unit of the FITC KSC SB RAS; Deputy Scientific Director of the Federal Research Center Krasnoyarsk Scientific Center SB RAS, Krasnoyarsk, Akademgorodok, Russia.
ORCID 0000-0001-9355-2872
Light-Harvesting Complex Studied
Via Time-Dependent Density Functional Theory-Based Calculations
E. A. Kovaleva 1, L. V. Begunovich 1, M. M. Korshunov 1, 2
Federal Research Center Krasnoyarsk Science Center SB RAS, Krasnoyarsk, Russia
Kirensky Institute of Physics, Federal Research Center Krasnoyarsk Science Center SB RAS, Krasnoyarsk, Russia
Time-dependent density functional theory-based approaches, TD-DFT and TD-DFTB, are used to study the optical absorption of B800 part of light-harvesting complex 2 (LH2) of Rhodoblastus acidophilus. Calculated spectra for both single molecule and the optimized structure of B800 complex containing nine of such molecules are in qualitative agreement with experimental data. The absence of any sizable effects originating from the interaction between adjacent molecules are proved. Thus, optical features of B800 LH2 part are not connected to the structural organization of pigments. The importance of the time-dependent procedure for the correct description of BChl a absorption spectrum is demonstrated.
Keywords: light-harvesting complex, purple bacteria, DFT, DFTB, TD-DFT, optical absorption spectra
Article received: 11.02.2025
Article accepted: 24.03.2025
1. Introduction
Photosynthesis is attracting much attention all around the world for decades. A key step in providing energy for subsequent biochemical reactions is the absorption of light by structures called light-harvesting (LH) complexes consisting of pigments linked by protein chains, see reviews [1–3]. LH2 peripheral light-harvesting complexes from the purple bacterium Rhodoblastus acidophilus is a widely used model object for studying LH absorption spectra [4–6] due to its relatively simple structure with the C9 symmetry, consisting of nine rhodopin β-D-glucoside and twenty-seven bacteriochlorophyll a (BChl a) molecules, linked into a single system by eighteen alternating amino acid chains. BChl a molecules are organized into two subsystems: the first subsystem is a close-packed ring of eighteen BChl a molecules oriented with porphyrin fragments along the symmetry axis of the structure, and the second subsystem is a loosely packed ring of nine BChl a molecules with porphyrin planes located perpendicular to the symmetry axis. The indicated subsystems are responsible for the characteristic peaks in the LH2 optical absorption spectrum, including the near-infrared absorption peaks, such as the Qy absorption peaks of BChl a molecules at 850 nm and 800 nm (the corresponding molecular subsystems are denoted as B850 and B800). As an alternative to the commonly used QM / MM approach, we propose it a simplified model to reproduce the LH2 optical properties. To study the LH system, as a first step, we model the B800 ring due to its simpler structure. The results obtained can be further utilized to construct more complex models and describe other parts of the LH complex.
Light-harvesting complexes are known to be difficult to characterize because interactions between pigments can lead to appearance of excitons in the system, as demonstrated for the B850 ring of the LH2 structure [7, 8]. Previously, possible exciton effects were not taken into account to create the LH2 model [9], since the emergence of collective excited states in the B800 ring is extremely unlikely due to the large distance between BChl a molecules [10]. It is assumed that the shift in the Qy peak position of B800 relative to that of the BChl a molecule is caused by the structure distortion of the magnesium-porphyrin fragments caused by interaction with protein residues. The present study is aimed to support this assumption using time-dependent (TD) calculations within the density functional theory (DFT) framework.
2. Computational methods
and models
The experimentally obtained 2FKW PDB structure [11] was used as a basis for our calculations, from which nine BChl a molecules forming the B800 ring were taken. The surrounding protein chains or their fragments were not included in the model to exclude the influence of the amino acid environment on the pigments, which made it possible to estimate the direct interaction between neighboring BChl a molecules. For comparison, the structure of an isolated pigment molecule was also calculated. Both structures were fully optimized until the forces acting on the atoms became less than 2 · 10−4 Hartree / bohr. The calculations were carried out in the DFTB+ software package using the DFTB3 version of the DFTB method, the standard set of 3OB parameters and the D3 correction for van-der-Waals interactions.
It has been previously found that the Hartree-Fock (HF) exchange has a significant effect on the optical properties of BChl a [9], therefore the hybrid exchange-correlation functional HSE06 was chosen for TD-DFT calculations in the VASP software package. The calculations were conducted under periodic boundary conditions. The lattice vector b was set to match the experimental distance between adjacent molecules in the B800 ring, which is 21.1 Å. A vacuum layer was introduced in other directions to prevent any artificial interactions between neighboring cells. The BChl a molecule was fully optimized using the GGA-PBE functional. The resulting structure was then used for hybrid calculations. The calculations employed a plane wave basis with a cutoff energy of 400 eV and the PAW method. Given the large size of the unit cell used in the calculations, computations at the Г-point is appropriate due to being both efficient and sufficient for an accurate description of the model.
To calculate the absorption coefficient, three different methods were applied depending on the software used. Due to the large number of atoms in the B800 ring system, only the TD-DFTB method was appropriate for its analysis. For the isolated BChl a molecule, both DFTB and standard DFT methods were utilized.
To calculate optical properties in VASP, the frequency-dependent dielectric matrix is determined. The absorption coefficient is calculated using the following formula:
σ(ω) = , (1)
where ε'(ω) and ε"(ω) are the real and imaginary parts of the dielectric function, and ω is the frequency. This approach is based on ground state calculations and does not include excited states. To address this limitation, a time-dependent (TD) procedure is required. The linear-response TD method involves solving the Casida equation:
Ω FI = ω2 FI , (2)
where Ω is the response matrix that depends on the occupied and virtual Kohn-Sham orbitals and the energy difference between them (ω), and FI is the eigenvector found by solving equation (2), which is used to calculate the oscillator strength.
The DFTB+ package implements both the Casida method and the real-time propagation of electron dynamics (ED). The time-dependent dipole moment µ depends on the electric field E as follows [12]:
µ(ω) = α E(ω), (3)
where α is the polarizability tensor. Imaginary part of the tensor trace α is proportional to the optical absorption coefficient:
σ(ω) = Im Tr (α). (4)
Here and below, calculations using the Casida method are marked as TD regardless of methods for the electronic structure calculations while the real-time propagation of electron dynamics is denoted as ED. HSE06 notation without indication of TD calculation corresponds to the calculation of the absorption coefficient from the frequency-dependent dielectric matrix.
3. Results and discussion
Previously discussed calculations of BChl a absorption spectrum [9] show the comparability of results obtained by hybrid DFT and parameterized DFTB3 method. The absorption spectrum contains both Soret peaks around 350 nm and characteristic peaks in the Q region. To describe the large molecular assemblies of more complicated LH2 models, the DFTB3 method is preferable due to its computational efficiency. The absorption spectrum of the B800 ring, consisting of nine BChl a molecules is identical to the spectrum of the isolated molecule (fig. 1) in the absence of an amino acid environment. The absorption peak Qy is located around 700 nm that is significantly different from the experimentally observed 800 nm, thus confirms our suggestion of the absence of any sizable interaction between molecules in B800 ring. Further the energies and intensities of optical transitions were obtained by solving the Casida equation within the DFTB and HSE06 electronic structure calculation methods (fig. 2).
The absorption spectra obtained by the TD-DFTB method are in agreement with the ED calculations and literature data, indicating the well-chosen and well-tested interatomic interaction parameters specifically designed to reproduce the properties of Mg-porphyrin compounds like chlorophyll. Only the lowest energy transition was calculated for the B800 ring corresponding to the Qy peak in order to save computational resources, since a large number of forbidden transitions with zero intensity significantly slow down the calculation. The obtained value of the Qy peak position is consistent with the data obtained by other methods (see Table 1). Thus, the bathochromic shift of the Qy peak in the absorption spectrum of B800 is entirely due to structural distortions rising from van-der-Waals interactions with protein chains.
It should be noted that TD-HSE06 calculation gives significant hypsochromic shift of both absorption peaks in the Q-region compared to those calculated from the frequency-dependent dielectric matrix. That indicates the need to carry out the non-stationary calculations for description of the optical properties of BChl a and similar pigments. In Figure 3, we demonstrate the absorption spectra of BChl a molecular calculated within DFTB3 and HSE06 approaches, as well as the results of DFTB calculations for the B800 ring. The position of Qy absorption peak is of particular interest since this peak is a characteristic feature of LH2 spectrum as a whole. All non-stationary calculations show close values of the Qy peak, located in the range of ~660–680 nm, while TD-HSE06 overestimates the transition energy for Qx peak (see Table 1).
4. Conclusion
Time-dependent DFT-based methods, DFTB3 and HSE06, were used to study the absorption spectra of BChl a molecule as the part of B800 ring of the LH2 complex of Rhodoblastus acidophilus. 1) It is shown that despite the absence of the collective excitations in the B800 system, the absence of any sizable effects connected to the interaction between pigments confirms the conjecture that the optical features of B800 are determined by the protein surroundings, not by their structural organization. 2) Use of the time-dependent calculations is necessary for the correct description of BChl a molecule absorption spectra since the ground state calculations underestimate the position Qy peak energy by 170 nm. 3) DFTB method gives reasonable results comparable to hybrid DFT method and may be used to model the larger systems containing magnesium-porphyrin compounds.
Acknowledgement
We thank V. F. Shabanov for useful discussions. Authors would like to thank Information Technology Centre, Novosibirsk State University for providing access to their supercomputers. L. V. Begunovich would like to thank Irkutsk Supercomputer Center of SB RAS for providing the access to HPC-cluster “Akademik V. M. Matrosov” (Irkutsk Supercomputer Center of SB RAS, Irkutsk: ISDCT SB RAS; http://hpc.icc.ru)
Authors contribution
E. A. Kovaleva – calculations, data processing, discussion, writing; L. V. Begunovich – resources, calculations, discussion; M. M. Korshunov – conceptualization, discussion, writing.
Funding
This work was supported by the state assignment of the Ministry of Science and Higher Education of the Russian Federation.
Conflict of interest
Authors declare no potential conflict of interest.
AUTHORS
Kovaleva Evgeniya A., Cand. of Sciences (Phys.&Math), e-mail: kovaleva.evgeniya1991@mail.ru; Senior Researcher, FITZ «Krasnoyarsk Scientific Center SB RAS», Krasnoyarsk, Akademgorodok, Russia.
ORCID 0000-0002-8008-0906
Begunovich Lyudmila V., Cand. of Sciences (Phys.&Math), Researcher, FITZ «Krasnoyarsk Scientific Center SB RAS», Krasnoyarsk, Akademgorodok, Russia.
ORCID 0000-0002-8103-1823
Korshunov Maxim M., Dr. of Sciences (Phys.&Math), Corr. Member of the RAS; Chief Researcher, L. V. Kirensky Institute of Physics of the RAS – a separate unit of the FITC KSC SB RAS; Deputy Scientific Director of the Federal Research Center Krasnoyarsk Scientific Center SB RAS, Krasnoyarsk, Akademgorodok, Russia.
ORCID 0000-0001-9355-2872
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